1. Field of the Invention
This invention relates generally to communication transmitters, receivers, and systems. More particularly, the invention relates modulation schemes that use pulse shaping filters with compact support in order to improve performance in a constrained bandwidth.
2. Description of the Related Art
It is known that continuous phase modulation (CPM) has superior spectral roll-off compared with linear modulation formats due to the phase continuity of the signals. Many different forms of CPM including, full and partial response CPM, multi-h and multi-T CPM formats, convolutional and trellis coded CPM, and nonlinear CPM have been discussed in the literature to improve the performance/bandwidth tradeoff of CPM signals.
In U.S. Pat. No. 7,532,676, a class of quadrature multiplexed continuous phase modulation (QM-CPM) signals that can reduce the already narrow bandwidth of regular CPM signals in half without sacrificing performance, has been introduced. The U.S. Pat. No. 7,532,676 is incorporated herein by reference. This patent provide further details on the generation of QM-CPM signals the component baseband message signals used in the generation of QM-CPM baseband signals. The QM-CPM signals are generated using a complex to real transformation on regular CPM signals. A simple transformation is used to extract two independent real signals from two independent CPM baseband signals, and then the two independent real signals are transmitted simultaneously on the two quadrature channels, generating a QM-CPM signal. The transformation considered in U.S. Pat. No. 7,532,676 to generate a real signal, m(t), from a regular CPM signal, mreg(t)=Aejα(t), that ism(t)=Re{mreg(t)}=A cos α(t)  (1)where A is the signal amplitude and α(t) is the phase variation of the regular CPM signal. It is known that m(t) has a finite state structure that can be derived from a real component of mreg(t) signals, which themselves are constant-amplitude complex signals whose phase follows a phase trellis. A QM-CPM signal, s(t), is then formed by two independent m(t) variations, m1(t)=Re{Aejα1(t)} and m2(t)=Re{Aejα2(t)}, where α1(t) and α2(t) correspond to two independent CPM phase functions generated by respective individual message sequences.
A low pass equivalent of a QM-MSK signal is given by:s(t)=m1(t)+jm2(t−τI,Q).  (2)Equation (2) is a lowpass equivalent of a bandpass signal where the real and imaginary parts of (2) are modulated onto quadrature sine/cosine carriers at a given carrier frequency. The component signals of QM-CPM, m1(t) and m2(t), which are essentially time varying pulse amplitude modulated (PAM) signals are referred to as CPM-PAM signals herein. The delay τI,Q in (2) is a relative time shift between the two CPM-PAM signals selected to minimize the PAPR value. It has been shown that QM-CPM signals can significantly improve the performance/bandwidth tradeoff of regular CPM signals. However, the performance gain is achieved at the expense of the constant envelope of CPM signals but with reasonably low peak to average power ratio (PAPR) values. For example, when the component regular CPM signals, mreg,1(t) and Mreg,2(t), are minimum shift keying (MSK) signals, the PAPR of the resulting QM-MSK signals can be made equal to 1.707 with a time shift τI,Q=T/2. The QM-CPM signals can be decoded by Viterbi decoding the two component CPM-PAM signals independently on I and Q channels.
Partial response CPM (PR-CPM) signaling has been used to improve the performance/bandwidth tradeoff of regular CPM signals. In PR-CPM, the effect of each symbol is spread over a pre-selected number of intervals L by selecting a baseband pulse of length LT. This is done using pre-filtering by passing the message through a pulse shaping filter prior to CPM modulation. Many different shapes of baseband pulses have been studied with PR-CPM in the literature.
It would be desirable to apply partial response signaling to improve the performance of QM-MSK signals. While one might consider generating partial response QM-CPM (PR-QM-CPM) by using a PR-CPM signal for mreg(t) in (1), it was found that this method does not generate PR-QM-CPM signals with attractive performance/bandwidth properties. Hence, it would be desirable to develop new ways to generate PR-CPM signals to overcome these problems. In regular PR-CPM, filtering is performed prior to modulation. It would be desirable to develop a PR-QM-CPM signaling scheme where a different type of filtering is performed after the QM-CPM modulation, i.e., after the m1(t) signal is formed as per (1) as opposed to being applied to α(t) as is done in the PR CPM art. It would be desirable to have methods and apparatus for signal generation, transmission, reception and detection/decoding of PR-QM-MSK signals.
Also, in linear baseband pulse amplitude modulation (PAM), that transmits symbols at the rate 1/T symbols/sec, Nyquist filtering is known to reduce the required bandwidth to ½T (or 1/T for two-sided carrier-PAM) while eliminating intersymbol interference (ISI) caused by the filtering. While Nyquist filtering limits the spreading in the frequency domain, it generates an infinitely long impulse response in the time domain that follows a sinc variation (where sinc(x)=(sin(πx))/πx). Raised cosine (RC) and square root raised cosine type filtering are more practical because they taper off the sinc variations faster so that a finite length impulse response filter can be used. However, RC signaling expands the bandwidth to a value (1+β)/2T, where β is called the roll-off factor. In such systems, the RC filter is often chosen so that the ISI equals zero at discrete sampling points spaced apart by T seconds, i.e., when sampled at the symbol rate, 1/T. Stated another way, with RC filtering, a received signal will be pre-processed so that upon sampling, a signal {circumflex over (x)}(kT+Δ) will be have all the ISI removed from it at the sampling times.
U.S. Pat. No. 5,916,315 is an example of another type of signaling scheme known as Partial Response Maximum Likelihood (PRML). In PRML processing, a PAM type data sequence is passed through a discrete time finite impulse response (FIR) filter or a channel that follows an FIR channel model. The FIR filtered data sequence is then passed through a square root RC filter. At the receiver, the received signal is passed through another square root RC filter. After the RC filtering (equalization) at the receiver, the received signal is sampled at the symbol rate, 1/T. With this choice of RC filtering, a controlled amount of intersymbol interference is left in the received and sampled signal. The received and sampled signal is known follow a fixed relationship at the discrete sampling points when sampled at a sampling rate Fs=1/T. For example, a PR2 channel model is defined by y(t)=0.5*x(t−2T)+x(t−T)+0.5x(t), or H(D)=0.5D2+D+0.5. Instead of trying to use an RC filter to remove this ISI, a Viterbi decoder is used to determine the most likely transmitted PAM sequence given the observations of the sampled signal, y(kT+Δ), where k is a discrete time index and Δ is a timing variable used in symbol timing recovery.
It would be desirable to develop Compact Pulse Shaping (CPS) filters to provide a CPS PAM/QAM signaling schemes without the need for RC equalization with longer RC filters at the receiver. It would be desirable for the CPS filter to have a relatively narrow bandwidth and to use subsequent digital processing to relax the need to cause zero intersymbol interference or a fixed relationship of intersymbol interference to exist at discrete sampling points of the received signal, y(t), i.e., at y(kT+Δ), where y(t) is sampled version of the received signal when sampled at a sampling rate Fs=1/T after being received through a communication channel.
It would be desirable to develop Viterbi decoder based receivers to optimally detect the CPS PAM/QAM signals in presence of the controlled amount of intersymbol interference (ISI) introduced by the CPS filter.